1 00:00:00,000 --> 00:00:05,000 Let's see, this room today are things like tutorials. 2 00:00:08,000 --> 00:00:14,000 And Greg asked me to do a tutorial on some of the things about GPS, 3 00:00:15,000 --> 00:00:21,000 not just GPS in the sense of what do you get when you go down to Key Mart and 4 00:00:21,000 --> 00:00:27,000 spend 250 bucks, but a little bit of tutorial on how GPS works, 5 00:00:28,000 --> 00:00:33,001 what it's all about, what are some of these other funny letters that you keep 6 00:00:33,001 --> 00:00:38,001 hearing about like SA and things like that, what are their attributes, 7 00:00:40,000 --> 00:00:47,000 to try to have so that the amateurs have a little 8 00:00:47,000 --> 00:00:52,000 bit better understanding of the system so that we can figure out new and 9 00:00:52,000 --> 00:00:53,001 interesting things to do with GPS. 10 00:00:56,000 --> 00:01:00,001 So Greg asked me for a title, and I didn't think very long when I came up with 11 00:01:00,001 --> 00:01:06,000 the one that appeared in the program of how does it work and why do I care. 12 00:01:07,000 --> 00:01:10,000 I'm not sure that I'll cover so many why do I cares, 13 00:01:11,001 --> 00:01:13,001 but there'll at least be a few. 14 00:01:16,000 --> 00:01:22,000 GPS of course is the global positioning system 15 00:01:23,000 --> 00:01:30,000 and we have to keep in mind through all of our discussions that GPS was built 16 00:01:30,000 --> 00:01:35,000 by the Department of Defense for military navigation and some other purposes. 17 00:01:36,000 --> 00:01:41,001 It is a military system and the military owns it and they have the keys to do 18 00:01:41,001 --> 00:01:46,001 everything and if they wanna do something, they will do it, even though in many 19 00:01:46,001 --> 00:01:50,000 cases, it may be a very stupid thing to do. 20 00:01:50,000 --> 00:01:56,000 In many cases, it may not make sense and in many cases, you will probably, during 21 00:01:56,000 --> 00:01:59,001 this little talk I'll give, here we make some irreverent 22 00:01:59,001 --> 00:02:01,001 comments about our military. 23 00:02:03,001 --> 00:02:08,001 That's okay, but I wanted to stress that. 24 00:02:11,001 --> 00:02:18,000 Navigation is really the key word in that and the military, 25 00:02:18,001 --> 00:02:21,000 navigation is a big thing. 26 00:02:21,001 --> 00:02:27,001 One of the things that I wanna stress to you all here right at the start is that 27 00:02:27,001 --> 00:02:32,001 navigation and time are very critically linked. 28 00:02:32,001 --> 00:02:36,000 All of the, when we talk about how GPS work, it's a timing system. 29 00:02:37,000 --> 00:02:42,000 When we talk about things that we do with GPS, it's one of the interesting 30 00:02:42,000 --> 00:02:44,000 applications is to distribute time. 31 00:02:46,001 --> 00:02:53,000 For those of you who are interested in navigation and interested in time, 32 00:02:53,001 --> 00:02:59,000 an absolute must read book, if you haven't read it, is a book by Davis Sobel. 33 00:03:00,000 --> 00:03:06,000 She wrote this book called Longitude and it describes 34 00:03:06,000 --> 00:03:12,001 the navigation problems of the 1700s. 35 00:03:12,001 --> 00:03:18,001 Now since amateurs are somewhat technically behind our time in terms of some of 36 00:03:18,001 --> 00:03:21,001 the things that go on, this may show a little of the applications 37 00:03:21,001 --> 00:03:23,000 of relevant technology. 38 00:03:23,001 --> 00:03:30,000 Specifically, it tells the story of John Harrison and his attempt to claim the 39 00:03:30,000 --> 00:03:35,001 prize that would allow ships to navigate into their home harbor safely. 40 00:03:37,000 --> 00:03:42,001 Tells the story in here of ships that were wrecked because they thought they were 41 00:03:42,001 --> 00:03:47,000 about ready to steam in home and ended up being 60 miles away. 42 00:03:49,000 --> 00:03:54,000 And needless to say, the appearance of reefs and rocks and so forth 60 miles 43 00:03:54,000 --> 00:03:55,001 away is a serious problem. 44 00:03:58,000 --> 00:04:02,000 The British government in the early 1700s 45 00:04:04,001 --> 00:04:10,001 earmarked a prize of, what was the amount then? 20,000 pounds, it's about $12 46 00:04:10,001 --> 00:04:17,001 million in today's currency to the first person who could come up with a way 47 00:04:18,000 --> 00:04:23,001 that ships could navigate safely to the equivalent of time of being able to keep 48 00:04:23,001 --> 00:04:28,000 time to an accuracy of about a minute after a long sea cruise. 49 00:04:29,001 --> 00:04:33,000 And for those of you who get turned on by navigation or clocks or 50 00:04:33,000 --> 00:04:35,000 anything else, really read this book. 51 00:04:35,000 --> 00:04:36,000 It's a fantastic book. 52 00:04:36,001 --> 00:04:38,001 I see a couple of people nodding yes, John do you agree? 53 00:04:39,000 --> 00:04:40,001 [...] sure if you finished it about a month ago, that's great. 54 00:04:43,000 --> 00:04:49,000 It's, I mean this was as good as Tom Clancy's idea that you can't put it down 55 00:04:49,000 --> 00:04:50,001 and you read until three o'clock in the morning. 56 00:04:51,000 --> 00:04:56,000 I want to discuss this whole thing on navigation by going back to the 1700s and 57 00:04:56,000 --> 00:05:00,001 showing a modern vintage 1700 APRS math. 58 00:05:05,000 --> 00:05:07,001 Because it illustrates a very interesting point. 59 00:05:08,000 --> 00:05:14,000 If you look at the map very critically, all of the features of, for instance, the 60 00:05:14,000 --> 00:05:17,000 New World were corrected in their locations North South. 61 00:05:18,000 --> 00:05:21,000 For instance, they knew where the mouth of the Amazon was. 62 00:05:22,000 --> 00:05:25,001 They knew the North South location of the bulge in Brazil. 63 00:05:26,000 --> 00:05:31,001 They knew the relative North South locations of all of the Caribbean islands with 64 00:05:31,001 --> 00:05:33,001 respect to Florida and the Keys. 65 00:05:34,000 --> 00:05:36,000 They knew where Chesapeake Bay was. 66 00:05:36,000 --> 00:05:40,001 They kind of missed a little bit out in the California area because they started 67 00:05:40,001 --> 00:05:46,001 sailing up the Gulf of California and found that it went a long 68 00:05:46,001 --> 00:05:48,001 ways and they didn't sail too far. 69 00:05:49,000 --> 00:05:52,001 And then they got up to the San Francisco area and started sailing South and 70 00:05:52,001 --> 00:05:55,000 found this big bay there and they thought the two were connected. 71 00:05:55,001 --> 00:05:58,001 That won't happen until the San Andreas Fault splits. 72 00:06:03,000 --> 00:06:05,000 They got the North South features right. 73 00:06:05,000 --> 00:06:07,000 They completely blew it East West. 74 00:06:07,001 --> 00:06:12,000 You can see that by looking at the shape of Africa, by looking at the width of 75 00:06:12,000 --> 00:06:19,000 India, by looking at where is Cape Town with respect 76 00:06:19,000 --> 00:06:22,001 to Italy in terms of our modern maps. 77 00:06:22,001 --> 00:06:24,000 They blew it East West. 78 00:06:24,000 --> 00:06:25,000 They got it North South. 79 00:06:25,000 --> 00:06:25,001 Why is that? 80 00:06:26,000 --> 00:06:31,000 With North South, you can measure your latitude when you're at sea with a 81 00:06:31,000 --> 00:06:33,000 relatively simple technique. 82 00:06:33,000 --> 00:06:38,000 You at least know what day it is and you can watch the sun from sunrise to sunset 83 00:06:38,000 --> 00:06:41,000 and find out what elevation does it get to at its highest angle. 84 00:06:42,001 --> 00:06:47,001 That and a simple essentially calendar tells you your latitude very accurately. 85 00:06:47,001 --> 00:06:49,001 You don't need any more information. 86 00:06:50,000 --> 00:06:55,000 The problem is that your East West location depends on having a precise time for 87 00:06:55,000 --> 00:07:00,000 sunrise or noon or some other external effect. 88 00:07:00,001 --> 00:07:06,001 And all of these East West errors that you see so evident on this map came 89 00:07:06,001 --> 00:07:11,000 because the mariners that were out there sailing around all of these 90 00:07:11,000 --> 00:07:12,001 places didn't know what time it was. 91 00:07:14,001 --> 00:07:21,001 So you look at a map like this and you see this absolutely critical relation 92 00:07:21,001 --> 00:07:27,000 of timing and navigation positions. 93 00:07:28,001 --> 00:07:30,001 And that's still there today. 94 00:07:31,001 --> 00:07:37,001 What we're gonna be talking about is systems where we measure, where we're 95 00:07:37,001 --> 00:07:40,001 located by using some timing information. 96 00:07:41,000 --> 00:07:47,000 Here is, unfortunately it's not the best view graph in the world but that's okay. 97 00:07:50,000 --> 00:07:52,001 Wanna give you a thought experiment. 98 00:07:53,000 --> 00:07:54,000 You've all done it. 99 00:07:54,000 --> 00:07:55,000 The lightning hits. 100 00:07:56,000 --> 00:07:57,000 You see the flash. 101 00:07:57,001 --> 00:07:58,001 You start counting seconds. 102 00:07:58,001 --> 00:08:00,000 How far are you away? 103 00:08:00,000 --> 00:08:04,001 You're a thousand feet per second away from it because the speed of sound is a 104 00:08:04,001 --> 00:08:09,000 thousand feet per second or about 300 meters per second. 105 00:08:09,000 --> 00:08:13,001 Now I'm gonna be in a lot of cases using metric measurements here. 106 00:08:13,001 --> 00:08:18,001 For those of you who, since I come from the Washington area, we have to be 107 00:08:18,001 --> 00:08:20,001 completely politically correct. 108 00:08:22,000 --> 00:08:28,000 And so we don't say, folks in the US don't know anything 109 00:08:28,000 --> 00:08:29,001 about the metric system. 110 00:08:30,000 --> 00:08:31,000 We're metric challenged. 111 00:08:32,000 --> 00:08:37,001 So for those of you who are metric challenged, a meter is a yard 112 00:08:37,001 --> 00:08:39,000 within about 10%. 113 00:08:40,000 --> 00:08:42,001 And a kilometer is a short mile. 114 00:08:43,001 --> 00:08:45,001 That sort of gets you in the right ballpark. 115 00:08:46,000 --> 00:08:50,000 I mean you're within factors of two or something when I say those things. 116 00:08:50,001 --> 00:08:54,001 Actually the meter equals a yard is correct or within 117 00:08:54,001 --> 00:08:56,000 10% so that's not a bad one. 118 00:08:58,000 --> 00:09:02,000 I found this, I have to tell a humorous story about myself here. 119 00:09:04,000 --> 00:09:05,001 Maybe you know I'm a radio astronomer. 120 00:09:06,000 --> 00:09:07,000 I'm a professional scientist. 121 00:09:07,001 --> 00:09:10,001 I remember a case in the early 1970s. 122 00:09:10,001 --> 00:09:16,001 I was in Sweden doing an experiment and we were using a radio telescope in Sweden 123 00:09:17,001 --> 00:09:24,000 and it's right on the sea coast and there was a storm coming in and I was left to 124 00:09:24,000 --> 00:09:31,000 run the telescope late at night and the people at the station told me, 125 00:09:31,000 --> 00:09:35,001 be sure to stow the telescope if the wind speed gets to be 25 meters per second. 126 00:09:36,001 --> 00:09:40,000 And it took me about three minutes of scratching to figure out whether 127 00:09:40,000 --> 00:09:41,001 that was a hard wind or a soft wind. 128 00:09:42,000 --> 00:09:43,001 I was metric challenged. 129 00:09:43,001 --> 00:09:50,001 I grew up with this antique system of units and the final conversion factor that 130 00:09:50,001 --> 00:09:54,000 clicked in my mind that made it so I could say, oh yeah, I know what that means 131 00:09:54,000 --> 00:09:59,000 was to think 60 miles an hour is 88 feet per second. 132 00:09:59,000 --> 00:10:00,001 I learned that in high school, algebra. 133 00:10:01,001 --> 00:10:06,000 And I could convert the feet to meters and that says, yeah, 134 00:10:06,000 --> 00:10:07,001 that's about a 50 mile an hour wind. 135 00:10:07,001 --> 00:10:10,001 That's when the wind, you know, I go outside and feel the wind getting 136 00:10:10,001 --> 00:10:12,000 to be high. 137 00:10:12,001 --> 00:10:17,001 Well, that came during the middle of an experiment where we were measuring some 138 00:10:17,001 --> 00:10:24,000 of the hydroxyl measures out in our galaxy and we were having 139 00:10:24,000 --> 00:10:27,000 to set the radial velocities in meters per second. 140 00:10:28,000 --> 00:10:32,000 So in my scientific world, I could think in terms of what frequency we had to set 141 00:10:32,000 --> 00:10:34,001 local oscillators to be able to receive this. 142 00:10:34,001 --> 00:10:39,001 But in terms of my physical realization, I had the problem of relating 25 meters 143 00:10:39,001 --> 00:10:41,001 per second into a hard wind versus a soft wind. 144 00:10:42,000 --> 00:10:45,000 We are metric challenged in this country and 145 00:10:45,000 --> 00:10:46,001 that's something that we gotta do something about. 146 00:10:47,001 --> 00:10:50,000 Okay, here's the Gennonkin experiment, thought experiment 147 00:10:50,000 --> 00:10:52,000 that I'm gonna suggest to you. 148 00:10:52,001 --> 00:10:53,001 The lightning hits. 149 00:10:54,000 --> 00:10:57,000 You're sitting there on two meters with your HT. 150 00:10:57,001 --> 00:10:59,001 Your names are Fred and Joe. 151 00:11:01,000 --> 00:11:07,000 And you're talking to two meters and you say, gee, that was a close one. 152 00:11:08,000 --> 00:11:13,000 I measured that as 4. 5 seconds, 4,500 feet away. 153 00:11:14,000 --> 00:11:16,000 And Joe says, gee, I did the same experiment. 154 00:11:17,000 --> 00:11:19,001 I measured it as about 5.7 seconds. 155 00:11:20,001 --> 00:11:25,001 Knowing where Fred lives and where Joe lives, we can then immediately know that 156 00:11:25,001 --> 00:11:28,000 there are only two places in the universe 157 00:11:28,000 --> 00:11:30,000 that that lightning crash could have hit. 158 00:11:30,001 --> 00:11:31,001 That's here and here. 159 00:11:32,000 --> 00:11:39,000 And because Fred happened to see the lightning crash out of his 160 00:11:39,000 --> 00:11:43,000 window and it was on the north side of the building, he knew that it had to be 161 00:11:43,000 --> 00:11:45,001 the north versus the south, one of those ambiguities. 162 00:11:46,000 --> 00:11:47,000 Now what did he make use of? 163 00:11:47,001 --> 00:11:53,000 Well, the timing signal, the event that started this was seeing the flash. 164 00:11:53,001 --> 00:11:59,001 The speed of light that conveyed the flash happening came to us at a speed of 300 165 00:11:59,001 --> 00:12:06,000 meters per microsecond, 1,000 feet per microsecond, one foot 166 00:12:06,000 --> 00:12:10,001 per nanosecond, for those of us who are metrically challenged, 167 00:12:10,001 --> 00:12:12,001 that's a nanosecond right there. 168 00:12:12,001 --> 00:12:17,000 I can remember Grace Hopper coming around and handing out nanosecond pieces of 169 00:12:17,000 --> 00:12:20,000 wire when she was talking about the HealthOS computers ran. 170 00:12:22,001 --> 00:12:25,001 So the speed of light compared to the speed of 171 00:12:25,001 --> 00:12:27,000 sound differ by a factor of a million. 172 00:12:28,000 --> 00:12:31,001 For those of you who are at Mike Japonas' talk, that's 10 to the sixth. 173 00:12:34,001 --> 00:12:39,001 At any rate, that is essentially instantaneous with respect to the 174 00:12:39,001 --> 00:12:41,000 sound velocity. 175 00:12:42,000 --> 00:12:46,001 So we actually had, in coming up with Fred and Joe being able to locate the 176 00:12:46,001 --> 00:12:49,001 lightning crash on the map, we had three pieces of information. 177 00:12:50,000 --> 00:12:56,001 We had a precise timing event that was perceived by our eye because it came at 178 00:12:56,001 --> 00:13:01,000 the speed of light, plus the two pieces of sound travel speed information. 179 00:13:01,001 --> 00:13:04,001 That was enough for us to be able to solve for the position. 180 00:13:06,000 --> 00:13:09,001 Now we could have turned that problem around and had both of these guys being 181 00:13:09,001 --> 00:13:16,001 transmitters and having the receiver be at that location and locate the position 182 00:13:16,001 --> 00:13:21,001 of the receiver, providing we have something that can measure both of the times. 183 00:13:22,000 --> 00:13:25,000 Otherwise, we can only measure the difference in arrival time. 184 00:13:26,000 --> 00:13:27,000 That's how the LAN works. 185 00:13:27,000 --> 00:13:34,000 Laran has a master transmitter that sits there at a frequency 186 00:13:34,000 --> 00:13:40,001 of about 100 kilohertz, transmitting a waveform that's about 10 pulses per second 187 00:13:40,001 --> 00:13:43,001 and you hear the master, then you hear the first 188 00:13:43,001 --> 00:13:45,000 slave and you measure that time interval. 189 00:13:46,000 --> 00:13:50,000 And you had the master and you hear the second slave and you measure that time 190 00:13:50,000 --> 00:13:55,000 interval and that sets up this kind of geometry here that allows you to locate 191 00:13:55,000 --> 00:13:58,000 where you are in a two dimensional flat world sense. 192 00:13:59,001 --> 00:14:04,001 Laran was the best navigation system that we had around up until 193 00:14:04,001 --> 00:14:06,001 about 15 years ago. 194 00:14:09,000 --> 00:14:15,000 It's been replaced by GPS, but that same concept applies to GPS because 195 00:14:15,000 --> 00:14:19,000 the GPS satellites are just clocks. 196 00:14:20,000 --> 00:14:24,000 For the purpose of this discussion, they are just clocks. 197 00:14:24,001 --> 00:14:30,000 They contain on board a cesium and in the case of the newest satellites that are 198 00:14:30,000 --> 00:14:34,000 going up in order to make them cheaper, that is a rubidium, there's actually a 199 00:14:34,000 --> 00:14:37,001 backup rubidium frequency standard on all of the present satellites with 200 00:14:37,001 --> 00:14:43,001 stability, accuracies, goodness of clocks at the levels of part and 10 to the 12 201 00:14:43,001 --> 00:14:45,001 through a part and 10 to the 13th. 202 00:14:46,001 --> 00:14:50,001 And that standard happens to be running at a frequency of 10.23 megahertz. 203 00:14:52,001 --> 00:14:59,001 And some of the critical things in here are that the 154th harmonic of that 204 00:14:59,001 --> 00:15:02,000 is the frequency that we listen to with GPS. 205 00:15:03,001 --> 00:15:08,001 And the code that we're gonna use as the principle code that we use is at 1 206 00:15:08,001 --> 00:15:10,001 .023 megabits per second. 207 00:15:11,000 --> 00:15:16,000 We don't have to do very much high math to realize that that's a 7490 208 00:15:16,000 --> 00:15:18,000 divider between those two. 209 00:15:22,000 --> 00:15:28,000 The sequence that transmits the primary timing information is a spread spectrum 210 00:15:28,000 --> 00:15:34,001 sequence that's 1023 bits long, going at a rate of 1.023 megabits per second says 211 00:15:34,001 --> 00:15:37,000 that that comes out once per millisecond. 212 00:15:38,000 --> 00:15:41,000 And then there's some other things like a 50-bit per second 213 00:15:41,000 --> 00:15:43,000 message and some other things. 214 00:15:43,000 --> 00:15:49,000 And I wanna just point out here because it will be important that those clocks in 215 00:15:49,000 --> 00:15:56,000 orbit are steered from the ground by the 216 00:15:56,000 --> 00:15:59,000 master clock at the US Naval Observatory here in the Washington 217 00:15:59,000 --> 00:16:03,000 area, at Al Gore's house. 218 00:16:06,001 --> 00:16:09,000 And the Naval Observatory keeps these clocks running to 219 00:16:09,000 --> 00:16:10,001 about the 10 nanosecond level. 220 00:16:11,000 --> 00:16:17,000 Okay, let me translate that set of words into a block diagram. 221 00:16:18,000 --> 00:16:25,000 Here is a block diagram of everything that is important to the small 222 00:16:25,000 --> 00:16:28,001 GPS user that's on the GPS satellite. 223 00:16:28,001 --> 00:16:30,001 All of the rest of the stuff is irrelevant. 224 00:16:31,000 --> 00:16:32,001 There's a bunch of other fancy things. 225 00:16:33,000 --> 00:16:33,001 We don't care about them. 226 00:16:34,001 --> 00:16:38,001 There's the 10.23 megahertz cesium and rubidium frequency standard. 227 00:16:39,000 --> 00:16:43,001 We'll come back and we'll talk about that box a little bit later, but that 10.23 228 00:16:43,001 --> 00:16:49,001 megahertz signal gets multiplied by 154 to make an L-band carrier at 229 00:16:49,001 --> 00:16:51,001 1575.42 megahertz. 230 00:16:52,000 --> 00:16:57,001 It's divided by 10 to give something that's gonna be a clock at 1 231 00:16:57,001 --> 00:16:59,001 .023 megabits per second. 232 00:17:01,000 --> 00:17:04,001 There's a computer that's involved in this because we're gonna have to keep all 233 00:17:04,001 --> 00:17:07,001 these guys synchronized and everything else. 234 00:17:09,000 --> 00:17:13,000 And we'll talk about some of these things that are important on that in a minute. 235 00:17:13,001 --> 00:17:20,000 There's a 10. 23 bit long pseudorandom noise sequence that 236 00:17:20,000 --> 00:17:23,000 has been a one millisecond repeat cycle. 237 00:17:24,000 --> 00:17:28,000 And that's used as a direct sequence spread spectrum code on this transmitter. 238 00:17:28,001 --> 00:17:34,001 That's combined with a 50 bit per second message which are combined. 239 00:17:35,000 --> 00:17:38,001 They're both digital so we can either think of them as being added or multiplied. 240 00:17:39,000 --> 00:17:40,000 It doesn't make any difference. 241 00:17:40,000 --> 00:17:45,000 And a module two adder which is called an exclusive OR gate which is then you, 242 00:17:45,000 --> 00:17:50,000 the polarity of the output of that is then used to flip the phase of the L-band 243 00:17:50,000 --> 00:17:57,000 transmitter in a BPSK signal and for simplicity think 244 00:17:57,000 --> 00:17:58,001 of that just as a doubly balanced mixer. 245 00:17:59,000 --> 00:18:01,000 Many circuits for about $7. 246 00:18:02,000 --> 00:18:05,000 The output of the doubly balanced mixer, we don't worry 247 00:18:05,000 --> 00:18:06,001 about filters and stuff like that. 248 00:18:06,001 --> 00:18:12,000 The simple block diagram goes to a big humongous power amplifier and is 249 00:18:12,000 --> 00:18:16,001 transmitted on the downlink on the circularly polarized antenna. 250 00:18:19,001 --> 00:18:23,001 On here, let's just talk about the characteristics of the 251 00:18:23,001 --> 00:18:25,000 digital signals that are in here. 252 00:18:26,000 --> 00:18:31,001 The 1.023 megabit per second sequence is, as I said, 10.23 bits long. 253 00:18:32,000 --> 00:18:35,001 The code that is used is called the gold code. 254 00:18:36,000 --> 00:18:41,000 It's derived from two different pseudo random 255 00:18:43,001 --> 00:18:48,000 sequence generators, 10 stage shift registers that are hooked up to 256 00:18:48,000 --> 00:18:49,001 give a pseudo random pattern. 257 00:18:50,001 --> 00:18:54,001 There are two of them, one of them that are the same on every GPS satellite. 258 00:18:55,001 --> 00:18:58,001 One of those, different taps on one of those. 259 00:18:58,001 --> 00:19:05,000 You can go along the shift register and pick out 10 different phases of the code. 260 00:19:05,001 --> 00:19:11,001 On one of those, you take and tap at an arbitrary shift register and then you tap 261 00:19:11,001 --> 00:19:15,001 that same one at a different point in the arbitrary shift register. 262 00:19:16,000 --> 00:19:19,000 That gives you 10 combinations of code on the first one. 263 00:19:19,001 --> 00:19:21,000 Then you got nine choices on the second. 264 00:19:21,001 --> 00:19:24,000 But because those are combined in the exclusive OR gate, that 265 00:19:24,000 --> 00:19:26,000 says it's really only half of that. 266 00:19:26,000 --> 00:19:31,000 That is 45 possible codes that describe all the GPS satellites. 267 00:19:31,000 --> 00:19:36,001 So it's 10 possibilities times nine possibilities, but 268 00:19:36,001 --> 00:19:38,000 you can flip those and they're the same. 269 00:19:38,000 --> 00:19:39,001 That means 45 possibilities. 270 00:19:40,001 --> 00:19:47,001 The GPS designers, the DOD folks in their infinite system picked 32 of 271 00:19:47,001 --> 00:19:53,000 those 45 codes and said, we will use these for all satellites in orbit. 272 00:19:54,001 --> 00:20:00,000 We will reserve another five of the codes for special purpose things. 273 00:20:00,000 --> 00:20:03,001 Things like pseudo lights and test transmitters and other fancy things. 274 00:20:04,000 --> 00:20:05,001 So that gets us up to 37. 275 00:20:07,000 --> 00:20:09,001 And they never talk about the other eight, but they're there. 276 00:20:11,001 --> 00:20:18,000 So they're really in fact 45 legal, all different codes that can be used 277 00:20:18,000 --> 00:20:22,000 and they only take selecting different taps on the shift register in order to be 278 00:20:22,000 --> 00:20:23,001 able to generate one versus the other. 279 00:20:24,001 --> 00:20:31,001 It's possible for you with about three ICs, maybe four to 280 00:20:31,001 --> 00:20:34,000 build a gold code generator. 281 00:20:34,001 --> 00:20:38,001 And if you have a 10 megahertz, a one megahertz clock, you can make 282 00:20:38,001 --> 00:20:40,000 your own GPS code generator. 283 00:20:40,000 --> 00:20:41,000 It's pretty simple. 284 00:20:44,000 --> 00:20:49,000 That code generator, every 20 cycles of that code generator, the 285 00:20:49,000 --> 00:20:50,001 phase may get flipped. 286 00:20:51,000 --> 00:20:52,001 Gotta realize this is just a phase flipper. 287 00:20:53,000 --> 00:20:54,000 It's an exclusive OR gate. 288 00:20:54,000 --> 00:21:00,000 And it's flipped by the data that comes out in something that's called the 289 00:21:00,000 --> 00:21:07,000 navigation message. 50 bits per second, that's 10.23, 1.023 megabits 290 00:21:07,000 --> 00:21:13,000 per second divided by 20460. 50 bit per second message, the 291 00:21:13,000 --> 00:21:14,001 message is 30 seconds long. 292 00:21:15,000 --> 00:21:16,001 That means 1500 bits. 293 00:21:17,001 --> 00:21:23,000 So in a sense, if you wanna think of this as a spread spectrum transmitter, it's 294 00:21:23,000 --> 00:21:26,001 a 50 bit per second message transmitter, is what the GPS is. 295 00:21:27,000 --> 00:21:33,000 But we're gonna make use of both the individual spreading code cycle 296 00:21:33,000 --> 00:21:35,000 clock as well as the data. 297 00:21:36,001 --> 00:21:40,000 So this is what the GPS satellite has in orbit. 298 00:21:40,000 --> 00:21:41,000 Pretty simple box. 299 00:21:41,001 --> 00:21:45,001 The up-light commands from the ground controllers are used to build 300 00:21:45,001 --> 00:21:47,000 things that go into that message. 301 00:21:49,000 --> 00:21:54,001 And we'll come back and talk in a little bit about what the SA phase didler does. 302 00:21:56,000 --> 00:21:58,000 Let me talk about the other side of it. 303 00:21:58,000 --> 00:21:59,001 What's in the GPS receiver? 304 00:22:01,000 --> 00:22:05,001 This is a generic block diagram of the receiver that's in one of these. 305 00:22:07,000 --> 00:22:12,000 It's the receiver that we're using in the TACs. 306 00:22:12,000 --> 00:22:14,000 It's every GPS receiver. 307 00:22:14,000 --> 00:22:19,000 First of all, there's a part of this that's analog that always scares people who 308 00:22:19,000 --> 00:22:26,000 tend to be digitally oriented, but it consists of an L band antenna, a low 309 00:22:26,000 --> 00:22:32,000 noise amplifier, also contained on this, a down converter mixer that comes off of 310 00:22:32,000 --> 00:22:36,000 a local oscillator that's got a fairly good crystal oscillator, goes through some 311 00:22:36,000 --> 00:22:39,001 set of IF stages and gets converted into a digital signal. 312 00:22:42,000 --> 00:22:47,000 We could have a long discussion, but it's quite adequate to simply have your 313 00:22:47,000 --> 00:22:49,000 analog to digital converter be a clipper. 314 00:22:49,000 --> 00:22:53,001 That is say, is the instantaneous polarity of the signal up or down? 315 00:22:55,001 --> 00:23:00,001 Some receivers, to get a little bit more sensitivity, use a two-bit sampler. 316 00:23:00,001 --> 00:23:04,000 I don't know of any GPS receivers out there that have more than two-bit 317 00:23:04,000 --> 00:23:06,000 samplers in their A to D converters. 318 00:23:06,000 --> 00:23:08,000 And this is directly sampling the IF. 319 00:23:09,000 --> 00:23:11,000 Now, what do we have to do to detect this? 320 00:23:11,001 --> 00:23:13,001 Well, let's give this some thought. 321 00:23:14,001 --> 00:23:17,000 The signal comes down from the GPS satellite. 322 00:23:17,001 --> 00:23:21,000 We don't know how far away the satellite is, so we don't know the code phase. 323 00:23:21,001 --> 00:23:26,000 So we're gonna have to somehow sit there and tune in code phase space in 324 00:23:26,000 --> 00:23:27,001 order to be able to extract the signal. 325 00:23:28,000 --> 00:23:30,000 But also, the satellite has a doppler shift. 326 00:23:30,001 --> 00:23:34,000 The signal from the satellite has a doppler shift, and in fact, also our first 327 00:23:34,000 --> 00:23:36,001 local oscillator may be at the wrong frequency. 328 00:23:36,001 --> 00:23:41,000 So we're gonna have to detect simultaneously in the frequency domain. 329 00:23:42,000 --> 00:23:46,001 We can generate a signal on the ground that matches the signal coming down from 330 00:23:46,001 --> 00:23:51,001 the GPS satellite, providing we can tune in two dimensions, time and 331 00:23:51,001 --> 00:23:53,000 frequency in terms of the code. 332 00:23:53,000 --> 00:23:55,000 Then we can generate our own replica. 333 00:23:56,000 --> 00:23:59,000 Then we can lock our replica on the incoming signal. 334 00:24:04,000 --> 00:24:08,001 And it's gonna be the parameters of that locking loop that are really the things 335 00:24:08,001 --> 00:24:11,000 that we use to extract all of the navigation data. 336 00:24:11,000 --> 00:24:17,000 That's typically done with essentially the schematic diagram that I show up here. 337 00:24:18,000 --> 00:24:20,001 The digital correlators are again exclusive OR gates. 338 00:24:20,001 --> 00:24:21,001 They multiply the signal. 339 00:24:22,001 --> 00:24:29,000 We end up with a two phase code generator that is making a replica of the 340 00:24:29,000 --> 00:24:36,000 code, and a two phase carrier oscillator, the two phases here are typically 341 00:24:36,000 --> 00:24:37,001 called prompt and early. 342 00:24:37,001 --> 00:24:41,000 They differ by one, or in some cases, not quite one, 343 00:24:41,000 --> 00:24:42,001 but a number similar to one bit. 344 00:24:45,000 --> 00:24:50,001 And in the frequency domain for the last local oscillator in the receiver, 345 00:24:51,000 --> 00:24:53,000 there's an in phase and a quadrature phase component. 346 00:24:54,000 --> 00:24:56,001 So we form all four possible products of those. 347 00:24:57,001 --> 00:25:03,000 Here in heavy lines, I formed one of them, which is the prompt bit of the code 348 00:25:03,001 --> 00:25:08,001 times the in phase bit of the oscillator, which I accumulate. 349 00:25:09,000 --> 00:25:10,000 This is just a counter. 350 00:25:11,000 --> 00:25:16,001 I count the number of times that these signals match versus the number of times 351 00:25:16,001 --> 00:25:22,001 that they don't match in a given period, and that can be done by just counting 352 00:25:22,001 --> 00:25:27,000 the number of ones that come out of that exclusive OR gate that occur 353 00:25:27,000 --> 00:25:28,001 during a given period of time. 354 00:25:29,001 --> 00:25:33,000 If the signals are perfectly correlated, they're either gonna match perfectly, so 355 00:25:33,000 --> 00:25:37,000 I'm gonna get all ones, or I'm gonna get all zeros because they 356 00:25:37,000 --> 00:25:38,001 match if they just happen to be out of phase. 357 00:25:39,000 --> 00:25:44,000 So all ones in that accumulator, or all zeros, means strong correlation. 358 00:25:44,001 --> 00:25:49,000 A number like a half of that in between says just noise. 359 00:25:50,001 --> 00:25:56,000 So I extract these four quadrature signals, quadrature in code and quadrature in 360 00:25:56,000 --> 00:26:01,000 local oscillator, and feed them down into something that's in essence a double 361 00:26:01,000 --> 00:26:04,000 digital signal processing costas loop. 362 00:26:06,000 --> 00:26:11,000 And use that to steer the phase and frequency of two numerically controlled 363 00:26:11,000 --> 00:26:13,000 oscillators, one that's generating the 364 00:26:13,000 --> 00:26:15,000 code, and one that's generating the carrier. 365 00:26:16,001 --> 00:26:21,000 Now, that costas loop is typically implemented in a microprocessor, but I show it 366 00:26:21,000 --> 00:26:27,001 here as a separate loop just for keeping in mind that it really is a digital way 367 00:26:27,001 --> 00:26:30,000 of making something that's sort of an analog process. 368 00:26:31,000 --> 00:26:38,000 The things like the carrier phase that's necessary to get 369 00:26:38,000 --> 00:26:44,000 the code match, the carrier phase necessary to get the carrier phase match, the 370 00:26:44,000 --> 00:26:50,001 polarity that comes out of the costas loop, the data polarity has in 371 00:26:50,001 --> 00:26:55,000 it that 50-bit per second message that we're gonna wanna decode. 372 00:26:55,001 --> 00:26:59,000 There's gonna be things like signal to noise ratio because on receivers like 373 00:26:59,000 --> 00:27:03,001 this, they got these neat little S-meter bars on it to tell how 374 00:27:03,001 --> 00:27:05,001 strong the signal is. 375 00:27:08,001 --> 00:27:11,001 So that somehow is intimately linked to a computer. 376 00:27:16,000 --> 00:27:19,000 The computer is running as a real-time computer. 377 00:27:20,000 --> 00:27:24,000 It's driven from the same clock that's controlling all of these other operations. 378 00:27:26,000 --> 00:27:30,001 And so I sort of show that link over here that that clock is probably derived 379 00:27:30,001 --> 00:27:32,001 from the same oscillator we see up here. 380 00:27:32,001 --> 00:27:36,001 So there's a timing clock as well as a frequency standard associated with that. 381 00:27:37,000 --> 00:27:41,000 And that real-time computer then after it gets all of this information and 382 00:27:41,000 --> 00:27:45,000 munches on it, talk a little in a minute about what munching it has to do, 383 00:27:45,000 --> 00:27:51,001 extracts the navigation data from the navigation message, performs 384 00:27:51,001 --> 00:27:55,001 PBT, that's position, velocity and time solution. 385 00:27:56,000 --> 00:27:58,000 We'll see why that's necessary in a minute. 386 00:27:58,001 --> 00:28:03,000 Displays the data to the user, talks to the outside world and whatever else it 387 00:28:03,000 --> 00:28:09,000 wants to do that is the place where the GPS receiver 388 00:28:09,000 --> 00:28:12,000 manufacturers put all their fancy whiz bang features. 389 00:28:12,000 --> 00:28:14,001 Does this drive an FCD panel, for instance? 390 00:28:14,001 --> 00:28:15,000 It may. 391 00:28:17,000 --> 00:28:22,001 And in the case of some of these receivers, which are important to us for one of 392 00:28:22,001 --> 00:28:27,000 the TAPR activities, that system timing clock may essentially have an output that 393 00:28:27,000 --> 00:28:29,000 is a one pulse per second signal. 394 00:28:30,000 --> 00:28:36,001 Now, let me, so that's what the 395 00:28:36,001 --> 00:28:38,001 transmitter and the receiver look like. 396 00:28:40,000 --> 00:28:45,000 Let me use a couple of word charts and then I'm gonna come back to the pictures. 397 00:28:46,000 --> 00:28:50,000 The way in which we do things with GPS, let's say we wanna find out where we're 398 00:28:50,000 --> 00:28:51,001 located and how fast we're moving. 399 00:28:52,001 --> 00:28:58,001 We measure the timing of several satellites 400 00:28:59,000 --> 00:29:02,000 with respect to our local internal clock. 401 00:29:03,001 --> 00:29:08,000 Our local clock's wrong in these cheap receivers, but at least we use the 402 00:29:08,000 --> 00:29:09,001 same clock for all of them. 403 00:29:11,001 --> 00:29:18,001 And the word that's usually used for that time difference 404 00:29:18,001 --> 00:29:24,001 between the satellite time that it's transmitting and what we perceive 405 00:29:24,001 --> 00:29:26,000 on the ground is called the pseudo range. 406 00:29:26,001 --> 00:29:30,001 It would actually be the range to the satellite if our local clock was set. 407 00:29:31,000 --> 00:29:34,001 Pseudo means not quite and the not quite is that 408 00:29:34,001 --> 00:29:36,000 our clock on the ground isn't perfect. 409 00:29:37,001 --> 00:29:43,001 If we take pseudo ranges to four satellites, that is a pair at times of four 410 00:29:43,001 --> 00:29:47,001 satellites and we know where the satellites are located. 411 00:29:48,000 --> 00:29:51,000 Now, the where are they located is transmitted to us as 412 00:29:51,000 --> 00:29:52,001 a part of this navigation message. 413 00:29:53,000 --> 00:29:56,000 Transmits down high accuracy Keplerian elements. 414 00:29:56,001 --> 00:30:02,000 We could use those four parameters to determine four parameters that apply to us. 415 00:30:02,000 --> 00:30:07,000 That is where we located in three dimensions, latitude, longitude, height, XYZ, 416 00:30:07,001 --> 00:30:11,000 or whatever other coordinates you wanna have, grid squares. 417 00:30:12,001 --> 00:30:17,001 And the fourth parameter is the error that's in your local timing clock that's 418 00:30:17,001 --> 00:30:19,000 inside the GPS receiver. 419 00:30:20,000 --> 00:30:23,001 If you're just navigating your boat, you really don't care about the timing 420 00:30:23,001 --> 00:30:28,000 error, so your receiver buries that down on screen number seven as to what time 421 00:30:28,000 --> 00:30:32,000 it is and doesn't tell you very much about it, but it had to solve for 422 00:30:32,000 --> 00:30:33,001 it in order to be able to make use of this. 423 00:30:33,001 --> 00:30:39,000 If you only wanted to do a two dimensional position, you're out on the ocean, you 424 00:30:39,000 --> 00:30:45,000 know your height because you know that mean sea level is determined more 425 00:30:45,000 --> 00:30:49,000 precisely even though there are waves and that kind of stuff. 426 00:30:49,000 --> 00:30:52,000 You know mean sea level more precisely than GPS is gonna 427 00:30:52,000 --> 00:30:53,001 find mean sea level for you. 428 00:30:53,001 --> 00:30:58,000 You only have to have three satellites because you only have to 429 00:30:58,000 --> 00:31:00,000 solve for your latitude and longitude. 430 00:31:00,000 --> 00:31:03,000 That's only two parameters and time being the third parameter. 431 00:31:05,000 --> 00:31:09,001 Also at the same time you make observations of the apparent frequency 432 00:31:09,001 --> 00:31:11,001 of the GPS satellites. 433 00:31:15,000 --> 00:31:20,001 Again, that apparent frequency is biased by things like the frequency error in 434 00:31:20,001 --> 00:31:23,000 the first local oscillator in your receiver. 435 00:31:24,000 --> 00:31:27,001 That's coming from the same thing that is the clock, so that's just 436 00:31:27,001 --> 00:31:29,001 how far off is the oscillator. 437 00:31:29,001 --> 00:31:34,001 So we call those pseudo range rates or apparent frequencies, 438 00:31:35,001 --> 00:31:37,000 apparent Doppler offsets. 439 00:31:38,000 --> 00:31:42,001 From that set of information, we can determine our three dimensional velocity, 440 00:31:43,001 --> 00:31:48,000 how fast are we moving and our local oscillator's frequency error. 441 00:31:51,001 --> 00:31:53,000 How well do we do that? 442 00:31:54,000 --> 00:31:59,000 Well, the signal that we're gonna finally use in the simple cheap dumb receivers, 443 00:31:59,000 --> 00:32:05,000 the Kmart receivers, is that CA code that stands for course acquisition. 444 00:32:05,000 --> 00:32:06,001 That's the 1023 bit code. 445 00:32:08,000 --> 00:32:14,000 And we can measure the code phase to a hundredth of a cycle if we're really good. 446 00:32:16,000 --> 00:32:19,000 Certainly a 30th of a cycle if we aren't very good. 447 00:32:19,000 --> 00:32:21,000 That's 10 degrees of electrical phase. 448 00:32:21,001 --> 00:32:26,001 Well, 3% of a microsecond is 30 nanoseconds. 449 00:32:26,001 --> 00:32:30,001 In time domain, which is 30 feet, which is 10 meters. 450 00:32:31,001 --> 00:32:33,000 And it may not be quite that good. 451 00:32:33,000 --> 00:32:38,001 I'll discuss PDOP in a minute, but sort of the 10 to 20 meters is how well can we 452 00:32:38,001 --> 00:32:40,001 measure each one of those guys typically. 453 00:32:43,000 --> 00:32:46,000 Now, let me continue this. 454 00:32:47,000 --> 00:32:53,001 So your GPS measure is the phase of that code to a fraction of the microsecond 455 00:32:54,000 --> 00:32:56,000 with respect to its internal clocks. 456 00:32:57,000 --> 00:33:03,000 The message contained information like the Keplerian satellite elements and those 457 00:33:03,000 --> 00:33:06,000 happen to be accurate to about 20 meters. 458 00:33:06,001 --> 00:33:08,000 How do they get those in there? 459 00:33:08,000 --> 00:33:12,000 It's not that the GPS satellite determines the coordinates, the position, the 460 00:33:12,000 --> 00:33:13,001 ephemeris, the Keplerian elements. 461 00:33:14,001 --> 00:33:19,000 It's that the ground determines that by observing GPS satellites 462 00:33:19,000 --> 00:33:20,001 and uplicking the information. 463 00:33:22,001 --> 00:33:27,000 And there's also a whole bunch of other information in that GPS message. 464 00:33:27,001 --> 00:33:32,001 So the GPS satellites are clocks and you compare them with 465 00:33:32,001 --> 00:33:34,000 your local clock on the ground. 466 00:33:37,001 --> 00:33:39,000 Let's see, we already did that one. 467 00:33:39,000 --> 00:33:45,001 Now, I told you I was gonna be irreverent to the military. 468 00:33:46,000 --> 00:33:51,001 The military, the DOD unfortunately imposes selective availability. 469 00:33:53,000 --> 00:33:57,000 Now, I will now give you the definitive statement as to just 470 00:33:57,000 --> 00:33:59,000 what is selective availability. 471 00:34:00,000 --> 00:34:02,000 And I'm gonna get back to my block diagram. 472 00:34:03,000 --> 00:34:07,000 Here is the block diagram of the spacecraft. 473 00:34:09,000 --> 00:34:13,000 In the output of that frequency standard, there's a phase diddler. 474 00:34:13,001 --> 00:34:17,000 Think of this as just a line stretcher, a piece of 475 00:34:17,000 --> 00:34:18,001 transmission line that you can stretch. 476 00:34:19,001 --> 00:34:24,001 And up in the GPS satellites, the DOD, because they go for such 477 00:34:24,001 --> 00:34:26,001 things, has trained a mouse. 478 00:34:28,000 --> 00:34:33,000 And the mouse is instructed to sit there and continually change 479 00:34:33,000 --> 00:34:35,000 the length of this line stretcher. 480 00:34:35,001 --> 00:34:41,001 He sits there and does this all day long, moving the line stretcher in and out. 481 00:34:42,000 --> 00:34:45,001 He does this according to a preset pattern. 482 00:34:46,000 --> 00:34:49,000 And he is told only do it so fast. 483 00:34:49,001 --> 00:34:51,001 Don't make your strokes too fast. 484 00:34:52,001 --> 00:34:56,000 And you can only go so far because your arms are only that long. 485 00:34:59,001 --> 00:35:04,000 So that's what the DOD does, is that they have this trained mouse sitting up 486 00:35:04,000 --> 00:35:07,001 there in the spacecraft doing its thing. 487 00:35:10,000 --> 00:35:17,000 He does it under the control of the spacecraft computer and he does it with a 488 00:35:17,000 --> 00:35:23,001 magic code that only other DOD smart mice know to do 489 00:35:23,001 --> 00:35:28,001 because they sit there on the ground and do just exactly the opposite of what the 490 00:35:28,001 --> 00:35:30,001 mouse in the spacecraft is gonna do. 491 00:35:34,000 --> 00:35:37,000 That's what SA is, selective availability. 492 00:35:38,000 --> 00:35:42,000 The military takes a perfectly good system, really a 493 00:35:42,000 --> 00:35:43,001 nice system and screws it up. 494 00:35:44,001 --> 00:35:51,000 And they do this in order to make this, have this mystique that it is a system 495 00:35:51,000 --> 00:35:55,000 that the military owns and you guys that are down here on 496 00:35:55,000 --> 00:35:56,001 the ground, you better remember it. 497 00:35:57,001 --> 00:35:58,001 Now what's the effect of that? 498 00:35:58,001 --> 00:36:02,001 Well first of all, depending on how fast mouse is sitting there doing his thing, 499 00:36:03,001 --> 00:36:06,000 that affects the velocities you see on the ground. 500 00:36:06,001 --> 00:36:11,000 Everybody who has a GPS receiver on the ground, they pull up to the stop light, 501 00:36:11,000 --> 00:36:14,000 they stop their car and the receiver still says they're moving 502 00:36:14,000 --> 00:36:16,000 2.3 miles per hour. 503 00:36:17,000 --> 00:36:19,000 That says how fast is the mouse's stroke. 504 00:36:21,000 --> 00:36:27,000 We also know that if you sit there and run a GPS receiver at a fixed location for 505 00:36:27,000 --> 00:36:29,001 a while, you'll find that you end up with the 506 00:36:29,001 --> 00:36:31,000 position wandering all over the place. 507 00:36:31,001 --> 00:36:37,000 Typically the peak error is about 100 meters and that's what the DOD sort of 508 00:36:37,000 --> 00:36:42,000 guarantees that they're gonna do almost all the time, but occasionally not, but 509 00:36:42,000 --> 00:36:44,000 that's assuming that you're seeing plenty of satellites. 510 00:36:45,000 --> 00:36:48,001 If you don't see very many satellites, you get hit a little bit worse. 511 00:36:50,000 --> 00:36:56,000 This is one of the biggest annoyances of the GPS system has been the fact that 512 00:36:56,000 --> 00:37:02,001 this perfectly good system funded by the military, funded by our taxpayers 513 00:37:02,001 --> 00:37:07,000 money, sits there and intentionally screws it up for all of the rest of us who 514 00:37:07,000 --> 00:37:09,000 are sitting there just trying to use it parasitically. 515 00:37:12,000 --> 00:37:14,001 So that's what selective availability is. 516 00:37:15,000 --> 00:37:19,001 You can see that it doesn't make me happy. 517 00:37:20,000 --> 00:37:25,000 It turns out that much of the effort, because the military puts selective 518 00:37:25,000 --> 00:37:31,000 availability on the GPS satellites, this is actually made a bit of blessing in 519 00:37:31,000 --> 00:37:38,000 disguise because its effects on the user on the ground are really very annoying. 520 00:37:38,001 --> 00:37:41,001 You know you're not moving 2.3 miles an hour 521 00:37:41,001 --> 00:37:43,000 when you're stopped at the stoplight. 522 00:37:44,000 --> 00:37:45,000 How do we fix that? 523 00:37:45,001 --> 00:37:47,001 Well, there are a couple of things that we can do to fix it. 524 00:37:47,001 --> 00:37:51,001 One is that we can go out and try to hire our own mouse, but the DOD doesn't like 525 00:37:51,001 --> 00:37:54,001 us to do that and they really keep tight control for these keys. 526 00:37:57,000 --> 00:38:01,001 Or we could be a little bit smart about this and do one of two things. 527 00:38:02,000 --> 00:38:07,001 One, first thing we can do is that we become smart users. 528 00:38:09,001 --> 00:38:16,000 The smart user and the receiver manufacturers have realized that the guy who buys 529 00:38:16,000 --> 00:38:19,000 this to use it on his boat is not gonna be a very smart user. 530 00:38:19,001 --> 00:38:24,000 The smart user can say, ah, each one of the mice 531 00:38:24,000 --> 00:38:25,001 is doing his own thing differently. 532 00:38:26,000 --> 00:38:30,000 The more mice I observe, the more I can start beating this 533 00:38:30,000 --> 00:38:31,001 down, square root of NFX. 534 00:38:32,000 --> 00:38:34,001 I don't use just four satellites, I use a bunch. 535 00:38:35,001 --> 00:38:39,000 But right now, as we'll see in a little bit, the constellation of GPS satellites 536 00:38:39,000 --> 00:38:43,000 is such that you almost always have seven or eight visible. 537 00:38:44,000 --> 00:38:48,000 So we can be smart users, we can tell our receiver manufacturers 538 00:38:48,000 --> 00:38:50,000 make your receivers smarter. 539 00:38:51,000 --> 00:38:57,001 The newest version of the Garmin, the GPS 2 Plus, is a 12 channel parallel. 540 00:38:58,000 --> 00:39:01,001 It's got 12 of those costus loops running in it simultaneously. 541 00:39:02,001 --> 00:39:05,001 And it uses every satellite it can find in the sky. 542 00:39:07,000 --> 00:39:11,001 As opposed to some of the earlier receivers, brands that I won't mention, but 543 00:39:11,001 --> 00:39:18,000 their color was yellow and they sold for high prices and are depicted in lots of 544 00:39:18,000 --> 00:39:23,000 advertisements, said, oh, I only need four 545 00:39:23,000 --> 00:39:24,001 satellites to make my position solution. 546 00:39:25,001 --> 00:39:29,001 I, my receiver, will decide which of the best four satellites to use and I will 547 00:39:29,001 --> 00:39:31,000 use those even though I can see more. 548 00:39:33,000 --> 00:39:35,000 So the receiver technology's improved. 549 00:39:35,001 --> 00:39:41,000 We've got a lot more stuff in the box that you can buy for $250 at Kmart now than 550 00:39:41,000 --> 00:39:45,001 was in the box that you would buy from Mr. Tribble, I'm sorry, the yellow box 551 00:39:45,001 --> 00:39:51,001 that you would buy six or seven years ago for $1,000. 552 00:39:52,000 --> 00:39:54,001 They're much better receivers, that's helped. 553 00:39:56,000 --> 00:40:00,000 We could be smart users, improve this a little bit more. 554 00:40:01,001 --> 00:40:07,000 One of the things is that, let's take one of the really frequent users of GPS for 555 00:40:07,000 --> 00:40:09,000 navigation are the boat owners. 556 00:40:10,000 --> 00:40:14,001 It's really neat when the fog sets in and you're out on Chesapeake Bay to know 557 00:40:14,001 --> 00:40:17,000 how to get back to the harbor. 558 00:40:18,000 --> 00:40:21,001 And this technology is absolutely superb for them. 559 00:40:22,001 --> 00:40:26,001 Unfortunately, the receiver manufacturers haven't realized one of the important 560 00:40:26,001 --> 00:40:30,000 facts that the boat users have and that is that they know how high they are. 561 00:40:30,000 --> 00:40:35,000 And these receivers, most receivers do not let you say, I'm in my position, 562 00:40:35,001 --> 00:40:39,000 you're gonna be able to find it, don't solve for my high, just solve for my 563 00:40:39,000 --> 00:40:42,001 latitude and longitude, that is a two dimensional position fix. 564 00:40:43,001 --> 00:40:46,001 That's a failing, I think, that a lot of the manufacturers still have. 565 00:40:47,000 --> 00:40:51,000 We'll come back to another fix that the users can do in a minute, but I wanna 566 00:40:51,000 --> 00:40:57,000 discuss a little how we, in my picture 567 00:40:57,000 --> 00:41:03,001 of Fred and Joe and the lightning bolt, we sort of indicated that at the place 568 00:41:03,001 --> 00:41:06,001 where these two curves cross, that determines the position. 569 00:41:07,000 --> 00:41:08,000 Well, how well does it do that? 570 00:41:08,001 --> 00:41:10,001 Well, here's a blown up sketch. 571 00:41:11,000 --> 00:41:14,001 There's always a measurement error associated with any of these processes and I 572 00:41:14,001 --> 00:41:20,000 tried to show the measurement error as being the width of the blue, the aqua and 573 00:41:20,000 --> 00:41:26,000 the red traces here, some intrinsic measurement precision, having to do with 574 00:41:26,000 --> 00:41:30,000 noise, the laws of physics, how cheap the receiver is and a whole bunch of other 575 00:41:30,000 --> 00:41:33,001 things as well as how good is the signals coming from the satellite. 576 00:41:34,001 --> 00:41:38,000 Now, when the two signals that you're trying, the two paths that you're trying to 577 00:41:38,000 --> 00:41:45,000 follow, or trying to use intersect at a fairly flat angle, then the 578 00:41:45,000 --> 00:41:48,000 width of the intersection can be very wide. 579 00:41:49,001 --> 00:41:54,000 In the opposite direction, I show this just as X and Y coordinates here, 580 00:41:54,001 --> 00:41:56,000 it can be very narrow. 581 00:41:56,001 --> 00:41:59,001 That is, it's an oblong shaped intersection. 582 00:42:00,001 --> 00:42:06,000 In the dimension that's bad, our precision, our measurement precision has been 583 00:42:06,000 --> 00:42:09,000 diluted by the geometry. 584 00:42:10,000 --> 00:42:15,000 You'll see on every GPS receiver the words, DOP, something DOP, and that means 585 00:42:15,000 --> 00:42:17,000 dilution of precision. 586 00:42:17,001 --> 00:42:24,001 That's purely a geometric number that says, how much wider is this in a given 587 00:42:24,001 --> 00:42:28,001 coordinate than is the intrinsic properties of the receiver? 588 00:42:29,001 --> 00:42:35,000 Dilution of precision, so X-DOP in this case, since this is the X coordinate 589 00:42:35,000 --> 00:42:40,001 going that way, the X-DOP uncertainty is about four, where the Y-DOP 590 00:42:40,001 --> 00:42:43,000 is a factor of about one. 591 00:42:45,000 --> 00:42:52,000 Now, for the GPS systems, what we get in the way of DOPs 592 00:42:52,000 --> 00:42:54,001 is dependent on how many satellites are visible. 593 00:42:54,001 --> 00:42:58,001 This is for, I think it was two days ago that I made the plot, it shows the 594 00:42:58,001 --> 00:43:02,000 number of satellites that are visible over a 24 hour 595 00:43:02,000 --> 00:43:04,001 period in Eastern Standard Time. 596 00:43:04,001 --> 00:43:09,000 For here in the Washington area, it actually is at my location, which is about 597 00:43:09,000 --> 00:43:10,001 20 kilometers from this location. 598 00:43:10,001 --> 00:43:16,000 That's about 15 or so miles for the metrically challenged. 599 00:43:17,001 --> 00:43:23,000 The number of satellites that's visible at any given time ranges from a low of 600 00:43:23,000 --> 00:43:27,000 four at slightly after 9 a.m. 601 00:43:27,001 --> 00:43:33,000 It's just about right now, up to a high of eight, if I can see 602 00:43:33,000 --> 00:43:34,001 the 15 degrees elevation. 603 00:43:35,001 --> 00:43:37,001 If I see lower, I'll see more satellites. 604 00:43:38,001 --> 00:43:42,001 That's out of a total constellation right now of 25 605 00:43:42,001 --> 00:43:44,001 satellites that are available. 606 00:43:45,000 --> 00:43:52,000 Now, the effect of that is that for horizontal determinations, the horizontal DOP 607 00:43:52,000 --> 00:43:53,001 through the day looks like this. 608 00:43:53,001 --> 00:43:56,001 Pretty low, it's a number varying from one to two. 609 00:43:57,001 --> 00:44:03,000 If a perfect system was capable of a 10 meter measurement, this says we 610 00:44:03,000 --> 00:44:05,000 get about 20 meters in the horizontal. 611 00:44:06,000 --> 00:44:08,001 Very small, very low numbers. 612 00:44:09,000 --> 00:44:12,001 That's again, computed for the same 15 degree elevation, computed 613 00:44:12,001 --> 00:44:14,000 for the Washington area. 614 00:44:14,001 --> 00:44:17,000 The highest peak that you see there is that 615 00:44:17,000 --> 00:44:18,001 time, there were only four satellites available. 616 00:44:19,000 --> 00:44:20,000 That's the one right there. 617 00:44:21,000 --> 00:44:25,000 So, horizontal measurements are always very good. 618 00:44:26,001 --> 00:44:31,000 Part of the reason for that is that the GPS satellites are over the entire sky 619 00:44:31,000 --> 00:44:34,000 and you'll end up with some north of you and some south of you and some 620 00:44:34,000 --> 00:44:35,001 east of you and some west of you. 621 00:44:36,000 --> 00:44:39,000 So, it's basically, you end up with lots of intersecting lines. 622 00:44:41,001 --> 00:44:47,000 If you look at the vertical, the how high am I, it's a much worse case. 623 00:44:49,000 --> 00:44:55,001 The vertical DOP can range up to a peak of six or 624 00:44:55,001 --> 00:44:57,000 seven for the same case. 625 00:44:58,001 --> 00:45:02,000 That case really had four satellites available as this isolated 626 00:45:02,000 --> 00:45:03,001 little spike at that time. 627 00:45:04,001 --> 00:45:11,001 And late in the evening, from about 10 p. m. local time to about two a.m. local 628 00:45:11,001 --> 00:45:13,001 time, it's pretty bad in this area. 629 00:45:14,001 --> 00:45:17,000 During part of the day, it's as good as possible. 630 00:45:17,000 --> 00:45:20,000 Two, but there are times during the day it gets as bad as six. 631 00:45:21,000 --> 00:45:27,001 In general, the vertical DOP is about three times worse than the horizontal DOP 632 00:45:27,001 --> 00:45:31,001 as a rule of thumb, but there are times that it's even worse than that. 633 00:45:32,000 --> 00:45:36,000 Part of the reason is that for the horizontal DOP, I said we had satellites 634 00:45:36,000 --> 00:45:40,001 north, south, east, and west of us that help pin this down real well horizontally 635 00:45:40,001 --> 00:45:42,001 in two dimensions, you know, all dimensions. 636 00:45:43,001 --> 00:45:46,001 To pick out our vertical, we have satellites that maybe are straight overhead 637 00:45:46,001 --> 00:45:48,001 going down to the horizon. 638 00:45:48,001 --> 00:45:50,000 We don't have any below our feet. 639 00:45:51,000 --> 00:45:57,000 So we only have one hemisphere of space to be able to determine things. 640 00:45:57,000 --> 00:45:59,001 And it's the missing bottom hemisphere, the fact 641 00:45:59,001 --> 00:46:01,000 that the Earth is not transparent. 642 00:46:02,000 --> 00:46:04,001 That makes it, is the fundamental reason why 643 00:46:04,001 --> 00:46:06,000 the vertical measurements are always poor. 644 00:46:07,001 --> 00:46:13,001 Now, in your receivers, in the messages coming out, you'll see also a 645 00:46:13,001 --> 00:46:15,000 parameter called PDOP. 646 00:46:16,000 --> 00:46:22,000 Here's the PDOP, that's overall position, dilution of precision, which is the 647 00:46:22,000 --> 00:46:28,001 combination of vertical DOP, root sum squared with horizontal DOP. 648 00:46:32,000 --> 00:46:36,000 So the PDOP is always worse than either of the other two. 649 00:46:36,001 --> 00:46:40,001 And I would basically recommend people look at H-DOP and D-DOP because it 650 00:46:40,001 --> 00:46:42,001 tells you really what the components are. 651 00:46:44,001 --> 00:46:48,000 One way that we can improve that situation is by having more satellites. 652 00:46:49,000 --> 00:46:54,000 I don't say that this is very feasible right now, but we can do much better if we 653 00:46:54,000 --> 00:46:56,001 use the other 19 navigation satellites that are 654 00:46:56,001 --> 00:46:59,000 available, which are the GLONASS satellites. 655 00:47:00,000 --> 00:47:05,000 Same period of time, the minimum number of satellites is seven, or 656 00:47:05,000 --> 00:47:06,001 nine a.m. whole. 657 00:47:07,000 --> 00:47:12,000 We now have 12 satellites instead of four because the Russian satellites happen 658 00:47:12,000 --> 00:47:15,000 to be at just the right place, and we hit a maximum of 14. 659 00:47:16,001 --> 00:47:22,000 So a lot of the reason that people do better if they happen to have a combined 660 00:47:22,000 --> 00:47:26,000 GPS and GLONASS system is just that there's a lot more satellites available. 661 00:47:26,001 --> 00:47:29,000 You double, essentially double the number of satellites. 662 00:47:29,001 --> 00:47:35,000 So where we, before, had a peak of eight, we now get a peak of 14, where we had a 663 00:47:35,000 --> 00:47:37,001 low of four, we now have a low of about seven. 664 00:47:39,001 --> 00:47:43,001 That doesn't say the GLONASS system is easy to use, and it doesn't say that you 665 00:47:43,001 --> 00:47:45,001 have cheap K-Mart receivers. 666 00:47:47,001 --> 00:47:52,001 Now let me talk about high accuracy GPS for a bit. 667 00:47:53,001 --> 00:47:56,000 I want to do this by predicating this with 668 00:47:56,000 --> 00:47:58,000 some comments about what I do for a living. 669 00:47:58,001 --> 00:48:00,000 I work for NASA. 670 00:48:01,000 --> 00:48:04,001 I direct a program at NASA called Very Long Baseline Interferometry. 671 00:48:04,001 --> 00:48:10,000 We use radio telescopes like this all around the world to make extremely high 672 00:48:10,000 --> 00:48:15,000 accuracy measurements of where these telescopes are located, how fast is the 673 00:48:15,000 --> 00:48:17,000 Earth spinning, how's it wobbling, and so forth. 674 00:48:19,001 --> 00:48:25,000 The accuracies we achieve on the better of our systems are down at levels of 675 00:48:25,000 --> 00:48:30,000 about three millimeters for 24 hours of observation and baselines that are 676 00:48:30,000 --> 00:48:32,001 six or seven thousand kilometers. 677 00:48:33,000 --> 00:48:39,001 Just to put that in context for the metrically challenged, the other unit that we 678 00:48:39,001 --> 00:48:43,000 talk about here is in the resolution and angle sense. 679 00:48:43,000 --> 00:48:49,001 You achieve angular accuracies of the order of a tenth or a 680 00:48:49,001 --> 00:48:51,001 20th of a milliarc second. 681 00:48:52,001 --> 00:48:59,000 A milliarc second, one milliarc second, is basically 682 00:48:59,000 --> 00:49:04,000 two centimeters, seen at 4,000 kilometers. 683 00:49:04,001 --> 00:49:09,000 The size of a quarter held over San Francisco is seen from here. 684 00:49:10,000 --> 00:49:16,000 The tenth or 20th that says that you can actually see George Washington's eye 685 00:49:16,000 --> 00:49:21,000 sockets on the quarter held over San Francisco viewed from here. 686 00:49:21,000 --> 00:49:24,001 With these techniques using these big radio telescopes, we can do that. 687 00:49:25,000 --> 00:49:30,001 This particular radio telescope is on the Big Island of Hawaii, that's one of the 688 00:49:30,001 --> 00:49:32,001 peaks, that's Mauna Kea in the background. 689 00:49:34,000 --> 00:49:39,000 This is a telescope that's operated by the National Radio Astronomy Observatory. 690 00:49:41,001 --> 00:49:46,000 I help coordinate the use of the, I'm really responsible for coordinating the use 691 00:49:46,000 --> 00:49:49,000 of these guys all around the world. 692 00:49:49,001 --> 00:49:54,000 Okay, we've been developing this technique for doing these high accuracy 693 00:49:54,000 --> 00:49:56,001 measurements over the last 20 or 25 years. 694 00:49:56,001 --> 00:49:59,001 The GPS people come along and say we can do almost as good and 695 00:49:59,001 --> 00:50:01,000 we can really do it a lot cheaper. 696 00:50:02,001 --> 00:50:07,000 And so a large part of my life has been trying to make sure I really understand 697 00:50:07,000 --> 00:50:10,001 how well GPS can do and to try to capitalize on the synergy 698 00:50:10,001 --> 00:50:12,000 of using the two systems together. 699 00:50:13,000 --> 00:50:20,000 In the high accuracy GPS world, I want to draw attention to this chart. 700 00:50:20,000 --> 00:50:22,001 This is pulled off of one of our web pages at Goddard. 701 00:50:22,001 --> 00:50:24,001 I'm sorry, it's slightly too wide to show. 702 00:50:26,000 --> 00:50:30,001 I want to point out that by post-processing the carrier phase data from dual 703 00:50:30,001 --> 00:50:35,001 frequency high accuracy receivers, surveyors and scientists routinely obtain 704 00:50:35,001 --> 00:50:39,000 results at the sub-centimeter level. 705 00:50:40,001 --> 00:50:45,001 Post-processing, that is you collect the data for a day, you somehow bring it 706 00:50:45,001 --> 00:50:49,001 back, you munch the data and you can get the centimeter level results. 707 00:50:50,001 --> 00:50:56,000 Dual frequency is to remove ionospheric biases and the GPS system actually has 708 00:50:56,000 --> 00:51:01,001 two down links, the L1 I described earlier and L2 which is at 1227 megahertz and 709 00:51:01,001 --> 00:51:03,001 yes there's been a lot of discussion about other 710 00:51:03,001 --> 00:51:05,001 frequencies, I won't go into that. 711 00:51:07,000 --> 00:51:11,001 The community around the world banded together to form an organization called the 712 00:51:11,001 --> 00:51:14,000 International GPS Service for Geodynamics. 713 00:51:16,000 --> 00:51:22,001 Data is logged in RINEX form transmitted by the internet from over 100 sites and 714 00:51:22,001 --> 00:51:26,000 results are typically available to the users within about 24 hours. 715 00:51:27,000 --> 00:51:33,001 Here's the map as of last week of these permanently 716 00:51:33,001 --> 00:51:39,001 operating tracking stations around the world that are contributing data that in 717 00:51:39,001 --> 00:51:43,001 general arrives within 24 hours although a few of them have some problems. 718 00:51:44,000 --> 00:51:48,001 It's still a little hard to get internet access to Krasnoyarsk reliably 719 00:51:48,001 --> 00:51:50,001 within 24 hours. 720 00:51:51,000 --> 00:51:56,001 Alma Ata and Bishtek in Kazakhstan and Kyrgyzstan are a little bit of a problem. 721 00:51:57,001 --> 00:52:03,000 Yerkutsk is a lot of problem getting data out and places like the Australian 722 00:52:03,000 --> 00:52:07,000 Davis and Casey sites in Antarctica it's a little problems getting the data out. 723 00:52:07,001 --> 00:52:10,001 But in general it's available within 24 hours, this 724 00:52:10,001 --> 00:52:12,001 is about 100 dots around the world. 725 00:52:12,001 --> 00:52:17,000 Ones that have little red dots in it are places that I've had some personal 726 00:52:17,000 --> 00:52:19,000 responsibility for making this network work. 727 00:52:19,001 --> 00:52:22,001 And you'll notice one of them is in Greenbelt just down the road here 728 00:52:22,001 --> 00:52:24,001 down the Baltimore, Washington, Parkway. 729 00:52:25,000 --> 00:52:27,000 I'll mention in a minute differential GPS. 730 00:52:27,001 --> 00:52:33,000 That Greenbelt line is the site of my differential GPS beacon that's on 145.79. 731 00:52:36,000 --> 00:52:40,001 The international service, the IGS, the International GPS Service for Geodynamics 732 00:52:40,001 --> 00:52:42,001 does scientific programs. 733 00:52:43,000 --> 00:52:46,001 It's all a collaborative effort, there's no big international money exchange, 734 00:52:46,001 --> 00:52:49,001 everything is funded by the local countries. 735 00:52:50,000 --> 00:52:54,001 But it gives global distribution for the data for programs like monitoring how 736 00:52:54,001 --> 00:52:58,000 the earth is deforming, how the earth spins and so forth. 737 00:52:58,000 --> 00:53:00,000 Things very similar to what I do with the very long 738 00:53:00,000 --> 00:53:01,001 baseline interferometry network. 739 00:53:03,000 --> 00:53:07,001 So it's justified by the science, international cooperative effort. 740 00:53:08,000 --> 00:53:12,001 If you want to see these web pages that I'm reproducing here it's cddisa 741 00:53:12,001 --> 00:53:15,000 .gsfc.nasa.gov. 742 00:53:18,000 --> 00:53:23,000 Second way that we beat selective availability and do better than we would have 743 00:53:23,000 --> 00:53:28,001 done under other conditions is by differential GPS. 744 00:53:29,000 --> 00:53:31,000 This is sort of going to be the last topic. 745 00:53:33,000 --> 00:53:39,001 Over here we have the typical user GPS receiver but to that we've added 746 00:53:39,001 --> 00:53:41,000 another element for the system. 747 00:53:42,000 --> 00:53:44,000 Here I'm showing it only observing four 748 00:53:44,000 --> 00:53:46,000 satellites, that's enough for the description. 749 00:53:46,001 --> 00:53:49,001 At some location we have a high quality GPS receiver. 750 00:53:50,000 --> 00:53:55,000 We know its location and we will tell the receiver what its 751 00:53:55,000 --> 00:53:56,001 location is, it's fixed. 752 00:53:57,001 --> 00:54:04,000 In the case of W3I-WI-13 it is the location of one of those hundred plus stations 753 00:54:04,000 --> 00:54:05,001 that was on the previous map. 754 00:54:07,000 --> 00:54:11,000 And it's running parasitically with a power splitter that's looking at the same 755 00:54:11,000 --> 00:54:14,000 antenna that provides data to that big network. 756 00:54:15,000 --> 00:54:20,001 Since the location is known, those pseudo ranges, delta T and the pseudo range 757 00:54:20,001 --> 00:54:26,000 rates, delta T dot for each of the satellites that are in view can be combined 758 00:54:26,000 --> 00:54:29,000 together and transmitted to some other user. 759 00:54:29,000 --> 00:54:31,000 They're combined together in a standard format. 760 00:54:32,000 --> 00:54:35,001 Most common format for this is called RTCM for Radio Technical 761 00:54:35,001 --> 00:54:37,000 Commission Maritime. 762 00:54:38,000 --> 00:54:44,001 SC104, subcommittee number 104, and a specification that they have set up that 763 00:54:44,001 --> 00:54:47,000 tells how will these bits be distributed. 764 00:54:48,000 --> 00:54:52,001 The actual message format is something that looks sort of like the GPS message 765 00:54:52,001 --> 00:54:58,000 format, which is a really bastard format to encode and decode, but 766 00:54:58,000 --> 00:54:59,001 at least it's been done many times. 767 00:55:00,000 --> 00:55:03,001 And that set of corrections are collected together and transmitted over some 768 00:55:03,001 --> 00:55:10,000 radio transmitter and the user has a second radio and applies those corrections 769 00:55:10,000 --> 00:55:14,000 directly to the observations, removing the errors. 770 00:55:15,000 --> 00:55:20,001 With differential GPS, that typical dumb, cheap receiver gets about one meter 771 00:55:20,001 --> 00:55:24,000 performance and the speed reads zero when you're stopped at the traffic light.